One of the more popular modifications to the Hele–Shaw cell (particularly in recent years) is to consider that the plates of the Hele–Shaw cell are no longer parallel but instead linearly tapered (either converging or diverging) in the direction of the flow. The concept was first introduced in [1]}, who considered tapered plates in channel geometry, discussed further in sec:Channel. Imposing tapered plates in radial geometry has been studied using linear stability analysis [2]}, weakly-nonlinear stability analysis [3]}, experimentally [2]}, [5]}, and by numerical simulations [6]}. Results indicate that tapering the gap between the plates either such that they converge or diverge can have a stabilising or de-stabilising effect on the interface depending on the injection rate. We use the numerical scheme presented in sec:NumericalScheme to study how tapering the plates while injecting at either a constant or time dependent injection rate can be used to reduce the development of viscous fingers in [7]}.
